Good question. I will add this to the FAQ section. We do this because we keep your submissions private to prevent cheating and the itch.io private submission process is complicated for many. (Zack)
The reason we ask for dropbox is because many people forget to allow access to the bbdoc file when using google drive. It's ends up being a lot of back and forth. It's much easier to simply use dropbox. We will accept Google Drive as well, but it helps to give access correctly when doing that.